A study was conducted to demonstrate the results of investigations into the modes of surface stability. A transversally isotropic uniform linearly elastic medium under uniform compression in three directions was considered for the investigations. The set of bifurcation equations of equilibrium was also investigated to evaluate the modes of surface stability. Investigations revealed that there was the plane deformation with displacements in the isotropy plane for the rotation stability loss and out of the isotropy plane for the volume type. The form of type 1 was implemented for an isotropic material and a weakly anisotropic material.